Complementary Logic Universe: Unique and Ordered Forms of 4-Valued Logic

[Organic]

Complementary Logic universe ( http://www.geocities.com/complementarytheory/BFC.pdf ) is an ordered logical forms that existing between a_XOR_b and a_AND_b.

For example:

Let XOR be #

Let AND be &

Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:

              Uncertainty
  <-Redundancy->^
    d  d  d  d  |
    #  #  #  #  |
    c  c  c  c  |
    #  #  #  #  |
    b  b  b  b  |
    #  #  #  #  |
   {a, a, a, a} V
    .  .  .  .
    |  |  |  |
    |  |  |  |
    |  |  |  | <--(First 4-valued logical form)
    |  |  |  |
    |  |  |  |
    |&_|&_|&_|_
    |
    ={x,x,x,x}


   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  | <--(Last 4-valued logical form)
    |#____|  |      
    |        |
    |#_______|
    |
    ={{{{x},x},x},x}

[b]
============>>>

                Uncertainty
  <-Redundancy->^
    d  d  d  d  |          d  d             d  d
    #  #  #  #  |          #  #             #  #        
    c  c  c  c  |          c  c             c  c
    #  #  #  #  |          #  #             #  #   
    b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
    #  #  #  #  |    #  #  #  #             #  #       #  #  #  #   
   {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |  |  |  |       |&_|_ |  |       |#_|  |  |       |&_|_ |&_|_
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |&_|&_|&_|_      |&____|&_|_      |&____|&_|_      |&____|____
    |                |                |                |
    {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}     
 
                                      c  c  c
                                      #  #  #      
          b  b                        b  b  b          b  b
          #  #                        #  #  #          #  #         
   {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |#_|  |&_|_      |#_|  |#_|       |  |  |  |       |&_|_ |  |
    |     |          |     |          |  |  |  |       |     |  |
    |     |          |     |          |&_|&_|_ |       |#____|  |
    |     |          |     |          |        |       |        |
    |&____|____      |&____|____      |#_______|       |#_______|
    |                |                |                |
    {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x} 

   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  |  
    |#____|  |      
    |        |
    |#_______|
    |    
    {{{{x},x},x},x}
[/b]

A 2-valued logic is:

    b   b 
    #   #    
    a   a     
    .   .   
    |   |   
    |&__|_   
    | 
    
    [B]a   b     
    .   .   
    |   |  <--- (Standard Math logical system fundamental building-block) 
    |#__|   
    |[/B]

We can see the triviality of Standard Math logical system,
when each n has several ordered logical forms between a_AND_b and a_XOR_b?

Please look at these ordered information forms http://www.geocities.com/complementarytheory/ETtable.pdf , but instead of numbers please look at them as infinitely many unique and ordered logical forms that are "waiting" to be explored and used by us.

I hope that it is understood that the flexibility of any language (including Math language) can be seen, when we examine it from the level of the information concept.

 

[matt grime]

Sorry if anyone thinks I'm fanning the flames. But in the last bit of code you seem to imply that those structures must correspond to the ordinary logical operations of xor, and and. I can see that the second one is axorb, but I don't see how even to read the first one as it looks like (a xor b)and(a xor b), which isn't a and b (consider a true b false).

 

[WWW]

Hi,

Maybe a,b,c,... are not true/false pairs but some version of multi-valued logic: http://en.wikipedia.org/wiki/Multi-valued_logic

you know, like probabilities in a QM wave function before it collapses to some certain state.

 

[WWW]

I thought about it, I think we can explain (a xor b) and (a xor b) like this:

(a xor b) and (a xor b) can hold if we do not have yet a (certain result a) xor (certain result b).

After we have some certain result then (a xor b) and (a xor b) collapsed to (a xor b) where each notation is a well defined logical state, which is our unique result.

 

[matt grime]

No, Organic, or WWW or whatever you choose to call yourself today, (a xor b) and(a xor b) iff (a xor b). It's not a hard thing to show that X and X is equivalent to X.

 

[WWW]

X and X is X but X has different degrees of probabilities when X = (a xor b) and (a xor b),
or when X = (a xor b).

For example:

X is a quantum element, which is a wave/particle duality.

a= wave

b= particle

X=(a xor b) and (a xor b) is X BOFORE it is collapsed to X=(a xor b)

If X=(a and b) then logically X cannot collapse to (a xor b).

If X=(a xor b) then logically X does not have a wave/particle duality.

The only way to show logically that X has a wave/particle duality that can collapse to (wave xor particle) is by this model:

( ((a xor b)and(a xor b)) xor (a xor b) )

 

[matt grime]

Seeing as you were attempting to explain how it modeled boolean logic in the degenerate case your argument is vacuous.

 

[WWW]

Can you use boolean logic to show a logical model of wave/particle duality, as I show in the previous post?

 

[matt grime]

DO you mean: can you write out a series of speciously linked words with no argument that makes no sense and still adheres to some alleged logical system? And for that to be boolean? As long as I'm allowed to draw whatever conclusion I wish without justification like you did then the answer must be yes, mustn't it?

 

[WWW]

Show us how you construct a model of X=wave/particle element that can collapse to (wave xor particle) state.

 

[matt grime]

As I don't believe you've done that, I don't see why I should. If you want just write out that thing you wrote above with itself referential circular logic in it and we'll call it boolean shall we?

Or how about

let A be the statement: X displays wave-like properties, let B be the statement X display particle-lke properties, then If X is say a photon, then Aand B is true...

i've no idea what you mean by model in this sense, and i suspect you couldn't tell me either

 

[WWW]

It is not fine what you write because:

If X=(wave and particle) then (wave and no-particle) or (no-wave and particle) --> no-X.

 

[matt grime]

did i say that displaying wave like properties means it is a wave? no i didn't. try reading it more carefully, i didn't say x is a wave nor did i say it was a particle, i said ti displayed proerties of both.

 

[WWW]

did i say that displaying wave like properties means it is a wave? no i didn't. try reading it more carefully, i didn't say x is a wave nor did i say it was a particle, i said ti displayed proerties of both.

I know.

And this is exactly why I wrote:

If X=(wave and particle) then (wave and no-particle) or (no-wave and particle) --> no-X.

What I show is that your model cannot describe X because by your model if one of the properties does not exist then (a and b)=0 --> X does not exist.

But as you know X can also be (a xor b).

 

[matt grime]

But I qualifed what X is, i said if it were a photon, for example, then... and you a and b are not the A and B that i have, reread the post and think...

 

[WWW]

Let A be the statement: X displays wave-like properties,
Let B be the statement X display particle-lke properties,

then If X is say a photon, then A and B is true...

You ignore the meaning of (A and B) properties, because these two properties are prevent/complement each other.

Therefore:
(A and B) are both 0(=prevent) and 1(=complement) --> ( ((A and B)=0) and ((A and B)=1) ), which does not hold in Boolean Logic.

The only way to show logically that X has a wave/particle duality that can collapse to (wave xor particle) is by this logical model:

( ((a xor b)and(a xor b)) xor (a xor b) )

 

[matt grime]

No they don't prevent each other, there is nothing necessarily stopping something displaying (some of) the properties of a wave and of a particle. for pity's sake a photon does that which means it is not a wave and it is not a particle it displays properties of both. according to you then the photon doesn't exist. displaying wave like properties does not preclude it displaying particle like properties, we have something that proves this is possible for heaven's sake.

 

[WWW]

Again you think trough Boolean Logic where any middle state is excluded.

A and B properties preventing each other existence not immediately but according
to our experiment.

Therefore A and B as Boolean model of X is a trivial logical system that does not hold, in this case.

 

[matt grime]

No, organic, doron, www, read what my statement A is, you don't appear to understand it. it displays wavelike properties. not it is a wave, but that it displays wavelike properties. a photon does that so that statement is true for a photon. or are you going to say that diffraction does happen. it also displays particle like properties as we know from einstein's experiment on the photovoltaic effect, therefore the assertion that a photon displays particle like properties is true. there for A and B is true in boolean logic... you seem to have it completely backwards, but that's true of a lot of your logic.

 

[WWW]

You know what?

Use Boolean Logic to say that X exists, but is this really all you want to Know about X?

Can you show us how you use Boolean Logic to explore a non-exluded-middle element like a photon for examlpe?

 

[WWW]

By Complementary Logic we can explore a non-excluded-middle elements, like Quantum elements, and find fine results, which are not just exist/not-exist Boolean Logic results.

Fuzzy Logic also does not fit here because its results cannot be both > 0.5 AND < 0.5 .


Only Complementary Logic can be in simultaneously in more then one logical state.

 

[matt grime]

you do understand that the statements a photon is a wave and a photon is a particle are both false don't you? you appear to be trying to make sometihng do that which it wasn't defined for. seeing as boolean logic has managed to deal with quantum mechanics for the last 80 years i don't think it's in much danger of being wrong do you?

 

[WWW]

Boolean Logic is a private case of excluded-middle logical system (0 xor 1).

Fuzzy Logic is an interpolation of (0 xor 1).


Both of them are used in QM but if we use a logical system that constructed on the idea of ordered complementary relations (like Complementary Logic), I think we have here a much better tool for QM.

 

[matt grime]

but you admit that you've not found a single way to use it so how can you make that specious claim?

 

[WWW]

I am not like an active scientist that has a laboratory, and he can use it to check theoretical methods.

But we have learned during the last 100 years that the power of simplicity that expressed through symmetry can be found in the basis of many interesting natural phenomena, for example:

Mendeleyev table (http://www.nfinity.com/~exile/periodic.htm ),

Hadrons family ( http://www.egglescliffe.org.uk/physics/particles/hadron1/hadron1.html ) ,

Fibonacci series ( http://goldennumber.net/links.htm )

Gauge theory (http://www.britannica.com/nobel/micro/228_45.html ) .

An example of Complementary Logic product is an ordered collection of symmetry break levels that can be found between multiset and "normal" set.

These kind of ordered collections includes infinitely many building-blocks that can be used by us for a lot of purposes for example: Natural numbers internal structures, local logical states of associations among opposite or many-valued logics, family connections between different information structures, and a lot of researches where symmetry and symmetry breaks involved.

I can continue to write on researches of complex systems and their relations with each others, and more and more, but as I said, this is not a one man's job.

Therefore I hoped to find some people that will take the ordered abstract models of symmetries that I suggested in my papers and will check it in their work.

I have found that many people are closed under the conceptual western false/true logic, and I know that there is still a very long way to go until, for example, persons like you Matt will be able to understand what I have to suggest.

But I do not really care because almost every day I discover the beauty that stands in the basis of simple ideas that are based on simple symmetries.

-------------------------------------------------------------------------------------------------

More to the point:

Let us check again my logical model of QM phenomena.

A=wave-like information

B=particle-like information

X= QM element


By Boolean Logic X=(A and B)

We know that a more accurate information of A is less accurate information about B and vise versa.

We want to define logical representations that do not ignore these preventing/complementing associations between A and B, which are two opposite properties of X.

An excluded-middle logical system of false/true reasoning is not rich enough to represent and explore X.

Shortly speaking, if we want to describe X, we need an included-middle logical system.

Complementary Logic (http://www.geocities.com/complementarytheory/BFC.pdf ) is a natural included-middle logical system, because it is based on the idea of simultaneous relations between preventing/complementing states.

Through this point of view we can show that 2-valued logic has at least 2 logical states:

The first state has redundancy_AND_uncertainty as nutural part of it.

The second state has no redundancy_AND_uncertainty as natural part of it.

Boolean logic, which is an excluded-middle logical system, has no redundancy_AND_uncertainty as a natural conceptual part of it.

Therefore it is not the right tool of explore X.

Please be aware that Complementary Logic is not limited to 2-valued logic.

It means that we can use it to construct very complex logical structures that have multi-valued logical states, for example look at these structures:
http://www.geocities.com/complementarytheory/ComplexTree.pdf

Instead of numbers, use the AND/XOR logical relations as demonstrated here:
http://www.geocities.com/complementarytheory/ConScript.pdf

Thank you.